Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

440×

body

valid

simplify294.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	14	6
1	29	4
2	50	4
3	70	3
4	82	3
5	125	3
6	229	3
7	321	3
8	336	3
9	434	3
10	786	3
11	3475	3
12	5001	3

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 3 (* y y) (* x x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 3 (* y y) (* x x))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(fma 3 (* y y) (* x x))

simplify57.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	59
1	84	52
2	267	52
3	1088	52
4	5001	52

prune28.0ms

Filtered

13 candidates to 10 candidates (23.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Merged error: 0.0b

Counts

15 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3 (* y y)) (* x x))
0.2b	(* 3 (* y y))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
36×	`associate-r`
28×	`fma-def`
23×	`*-un-lft-identity`
16×	`associate-l`
15×	`add-cube-cbrt`
14×	`unswap-sqr`
8×	`swap-sqr`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`*-commutative`
4×	`distribute-lft-out` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

2 → 84

Calls

2 calls:

31.0ms	(+ (* 3 (* y y)) (* x x))
9.0ms	(* 3 (* y y))

series59.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* 3 (* y y)) (* x x))
26.0ms	(* 3 (* y y))

simplify44.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	230	238
1	1051	218
2	5002	208

prune109.0ms

Filtered

90 candidates to 56 candidates (37.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	3	0	3
Picked	0	1	1
Done	1	0	1
Total	91	4	95

Merged error: 0b

Counts

95 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (fabs y) 3) (sqrt (* y y))) (* x x))
0.2b	(* (* (fabs y) 3) (sqrt (* y y)))
18.7b	(sqrt (* y y))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
65×	`sqrt-prod`
51×	`associate-r`
48×	`associate-l`
47×	`fma-def`
46×	`unswap-sqr`
39×	`*-un-lft-identity`
27×	`add-cube-cbrt`
16×	`pow1`
14×	`swap-sqr`
12×	`*-commutative`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-pow1` `distribute-lft-out`
5×	`rem-sqrt-square` `add-log-exp`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `pow1/2` `sum-log` `pow-sqr` `pow-prod-up` `flip-+`

Counts

3 → 160

Calls

3 calls:

54.0ms	(+ (* (* (fabs y) 3) (sqrt (* y y))) (* x x))
16.0ms	(* (* (fabs y) 3) (sqrt (* y y)))
5.0ms	(sqrt (* y y))

series115.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* (* (fabs y) 3) (sqrt (* y y))) (* x x))
49.0ms	(* (* (fabs y) 3) (sqrt (* y y)))
9.0ms	(sqrt (* y y))

simplify55.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	345	665
1	1327	599
2	5001	549

prune265.0ms

Filtered

169 candidates to 110 candidates (34.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Merged error: 0b

Counts

173 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3))) (* x x))
0.1b	(* (fabs y) (* (cbrt 3) (cbrt 3)))
0.2b	(* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3)))
0.3b	(* (fabs y) (cbrt 3))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

388×	`add-sqr-sqrt`
235×	`unswap-sqr`
149×	`associate-r`
134×	`cbrt-prod`
133×	`associate-l`
95×	`fma-def`
74×	`add-cbrt-cube`
68×	`cbrt-unprod`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`swap-sqr`
32×	`pow1` `add-exp-log`
20×	`*-commutative`
19×	`pow-prod-down` `prod-exp`
6×	`distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 327

Calls

4 calls:

105.0ms	(+ (* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3))) (* x x))
14.0ms	(* (fabs y) (* (cbrt 3) (cbrt 3)))
36.0ms	(* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3)))
5.0ms	(* (fabs y) (cbrt 3))

series316.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3))) (* x x))
65.0ms	(* (fabs y) (* (cbrt 3) (cbrt 3)))
95.0ms	(* (* (fabs y) (* (cbrt 3) (cbrt 3))) (* (fabs y) (cbrt 3)))
45.0ms	(* (fabs y) (cbrt 3))

simplify141.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	760	2571
1	4183	2185
2	5001	1890

prune607.0ms

Filtered

339 candidates to 219 candidates (35.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	338	1	339
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	339	4	343

Merged error: 0b

Counts

343 → 4

regimes73.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample558.0ms

Algorithm

intervals

Results

335.0ms

14197×

body

valid